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Iterative Optimization in Inverse Problems

Charles Byrne
€210.80
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A01=Charles Byrne
advanced optimization techniques for imaging
algorithm
and statistical estimation
Art Algorithm
Author_Charles Byrne
Auxiliary Function
auxiliary function methods
Barrier Function Methods
barrier- and penalty-function methods
Bounded Level Sets
Bregman Distance
Category=PBKJ
Cimmino's Algorithm
Cimmino’s Algorithm
closed
Closed Convex Set
convex
convex feasibility problems
Convex Function
Convex Sets
CQ Algorithm
EMML
EMML Algorithm
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
expectation
fixed-point algorithms
fixed-point iteration
forward-backward splitting
function
Induced Matrix Norm
iterative algorithms for medical imaging
Kl Distance
Kth Step
Kullback Leibler Distance
landweber
Landweber Algorithm
Logarithmic Barrier Function
Nonempty Convex Subset
Nonnegative Solutions
optimization
penalty function approach
Penalty Function Methods
Projected Gradient Descent
proximal algorithms
proximal minimization
sequential optimization
Sequential Optimization Methods
set
SFP
starting
Starting Vector X0
step
subclasses of auxiliary-function methods
SUMMA algorithms
variational inequality algorithms
vector

Product details

  • ISBN 9781482222333
  • Weight: 544g
  • Dimensions: 156 x 234mm
  • Publication Date: 12 Feb 2014
  • Publisher: Taylor & Francis Inc
  • Publication City/Country: US
  • Product Form: Hardback
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Description

Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author’s considerable research in the field, including his recently developed class of SUMMA algorithms. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing.

Organizing the topics from general to more specific, the book first gives an overview of sequential optimization, the subclasses of auxiliary-function methods, and the SUMMA algorithms. The next three chapters present particular examples in more detail, including barrier- and penalty-function methods, proximal minimization, and forward-backward splitting. The author also focuses on fixed-point algorithms for operators on Euclidean space and then extends the discussion to include distance measures other than the usual Euclidean distance. In the final chapters, specific problems illustrate the use of iterative methods previously discussed. Most chapters contain exercises that introduce new ideas and make the book suitable for self-study.

Unifying a variety of seemingly disparate algorithms, the book shows how to derive new properties of algorithms by comparing known properties of other algorithms. This unifying approach also helps researchers—from statisticians working on parameter estimation to image scientists processing scanning data to mathematicians involved in theoretical and applied optimization—discover useful related algorithms in areas outside of their expertise.

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